6 Answers
6

Currently the nameSanta Claus is approximately 10 times more popular than Father Christmas in the United States, but there was a time when their popularity was similar. In addition, the popularity of those two names had tracked together in the UK until the mid 1980's.

Letter to Virginia (O'Hanlan), Francis P. Church, New York Sun,
1897--"Yes Virginia. There is a Santa Claus."

The image of Santa Claus now becomes varied and often elfin,
rejecting Nast's robust figure. The Oz illustrator W. W. Denslow drew
Santas of Munchkin-size. Arthur Rackham, an artist and illustrator of
children's books drew Santa as an elf.

Norman Rockwell drew full-sized Santas for the Saturday Evening Post.

Archie Lee of the D'Arcy Advertising Agency proposed a realistic,
modern appearing Santa Claus with red cheeks and wrinkled face, but
appearing vital and young, for Coca Cola. This image was painted in
oil by a commercial illustrator Hadden H.Sundblom, starting with the
1931 holiday promotion. The original model was Lou Prentice, a retired
salesman who died shortly thereafter. This is the Santa Claus we know
today.

The name Santa Claus has become a well developed cultural icon, and we discover an intentional development in the article Santa Claus Does More than Deliver Toys, in the Journal Consumption Markets Culture pages 207-240:

Society's collective memory of Santa Claus reflects the dynamic and
interactive process between advertising, as well as other cultural
institutions, and consumers. Coca-Cola's advertising has maintained,
transformed and mass-produced the image of Santa Claus over time.
Consumers have numerous experiences with Santa Claus— they have
watched, listened, read, and even dreamed of Santa Claus. As consumers
experience Santa, they actively combine and adapt cultural discourse
to fit with their individual, familial, and cultural traditions.

The name Santa Claus benefits news papers, magazines, movies, merchants, politicians, and just about everyone in our country. Saint Nicholas is surely welcome in the United States, and we definitely prefer to call him Santa, but he has Nicknames too:

Santa Claus, also known as Saint Nicholas, Father Christmas, Kris
Kringle and simply "Santa..."

The monicker Father Christmas competes with Saint Nicholas, and is a more popular than either Kris Kringle or Saint Nick. Traditionalist can argue about whether it should be, but in the United States, Santa Claus and Father Christmas are both the mythologized historical Saint Nicholas.

The name Father Christmas is just as popular today as it was in 1922. Barbara Reeds published a Christmas story called *Father Christmas* in 1995. At Amazon.com the book, Father Christmas BC is among the many books available promoting Father Christmas as Santa.

Perhaps the most well known recent reference to Father Christmas is in the movie adaptation of C.S. Lewis's The Chronicles of Narnia: The Lion, the Witch and the Wardrobe (2005), where Father Christmas accosts the children, announces that Christmas has returned to Narnia and gives them powerful gifts that will factor into the rest of the stories. The fact that C.S. Lewis and J.R.R. Tolkien, who also has a popular book entitled Father Christmas, are British authors does not diminish their influence on American culture.

Conclusion

Father Christmas and Santa Claus were equally popular names in the British Empire that spawned the American dream, and so it is no surprise that both names were popular in the early days of the United States. Father Christmas has not become a less popular name, but cultural developments have made Santa Claus a more popular name.

As this ngram shows, the term has very little usage in US print as compared to Santa Claus. There is a slight rise in usage over the years, but a quick scan of the listed works often refer to historic works or the British tradition.

Most US listeners would probably understand a reference to Father Christmas, but most would probably consider it a bit archaic, stilted or reference to a foreign tradition.

If corpus evidence is anything to go by, then Santa Claus is more popular than Father Christmas in the US, and Father Christmas is more popular than Santa Claus in the UK, but by a very much smaller degree. The COCA shows Santa Claus as being 27 times more frequent than Father Christmas, whereas the BNC shows Father Christmas as being just under twice as frequent as Santa Claus.

To answer part one of your question: In the US, the name Santa Claus is by far the most widespread and popular.

As to the second part of your question: If you say "Father Christmas", and you have a foreign accent, (esp. British) it will not sound unusual, nor will you be laughed at. If you say "Father Christmas" with a Brooklyn accent, it will not only sound unusual, but people will be rolling on the floor.

The American Santa Claus is generally considered to have been the invention of Washington Irving and other early nineteenth-century New Yorkers, who wished to create a benign figure that might help calm down riotous Christmas celebrations and refocus them on the family.

This new Santa Claus seems to have been largely inspired by the Dutch tradition of a gift-giving Sinterklaas, but it always was divergent from this tradition and was increasingly so over the course of the nineteenth and twentieth centuries. So, the American Santa is a largely secular visitor who arrives at Christmas, not the 6 December; who dresses in furs rather than a version of bishop's robes; who is rotund rather than thin; and who has a team of flying reindeer rather than a flying horse.

At first his image was somewhat variable, but Thomas Nast's illustrations for Harper's Illustrated Weekly (1863-6) helped establish a figure who looks fairly close to the modern Santa. This figure was taken up by various advertisers, including Coca-Cola, with the result that he is now the 'standard' version of the Christmas visitor and has largely replaced the traditional Father Christmas in England.

The English Father Christmas seems to have had an entirely separate origin from Sinterklaas, being a personification of Christmas and a Yule-tide visitor - not a gift-giver - rather than a version of St Nicholas.

The earliest reference to him comes from the mid-fifteenth century, when a Sir Christëmas appears in a carol, although most discussions start with Ben Johnson's early seventeenth-century old or Captaine Christmas. Whilst strenuous efforts were made by the puritans of the seventeenth century to do away with this character, they did not succeed.

In the nineteenth century Father Christmas benefitted from the general Victorian revival of Christmas and can be found in, for example, Dickens' Christmas Carol. However, from the 1870s onwards Father Christmas became increasingly like the American Santa Claus, both in terms of his actions - he started giving gifts - and his appearance, with the result that two are nowadays virtually inter-changeable.